Phrases like "either… or", "neither… nor", "if… then… else…", "between… and… (inclusive)", and "nothing if not" explicitly use multiple different logic operators. Some of these logic operators (such as "neither", "nor", and "inclusive") are rarely used in informal speech. Similarly, informal speech rarely uses so many different logic operators in a single expression. These are hints that these logic operators are being used to express formal logic, and the meaning can be derived logically.
Here are the assumptions:
1) <X> exists.
2) <X> is nothing if not <Y>.
We seek to prove that:
3) <X> is at the very least <Y>, and
4) <X> is certainly <Y>.
The argument is fairly straight-forward:
5) Either <X> has the feature <Y>, or
6) <X> does not have the feature <Y>
7) If (6) is true, then <X> "is nothing", per (2).
8) If <X> "is nothing", then it does not exist.
9) But we have assumed that <X> exists, per (1), so neither (8), nor (7), nor (6) can be true.
10) Therefore (5) is true. We know that <X> has feature <Y>.
11) We have proved that <X> is certainly <Y>.
12) Since the assumptions state nothing else about what <X> is, or is not, we have not proved that <X> is more than <Y>, nor have we proved that <X> is <Z>.
13) We can only state with certainty that <X> is at the very least <Y>.
14) Q.E.D.